Output feedback preview tracking control for time‐varying polytopic descriptor systems

Abstract

Summary This paper focuses on the problem of static output feedback preview tracking control for discrete‐time descriptor systems with time‐varying parameters subject to a previewable reference signal. First, an augmented error system including the information of the future reference signal is constructed based on the error system approach. Second, a preview control policy is constructed by integrating output feedback, preview action, and integral operation. Relying on the augmentation modeling technique, a linear preview control design problem is transformed into an equivalent augmented output‐feedback control design problem. New design conditions guaranteeing the existence of a stabilizing controller are recast as an LMI‐based feasibility problem. The proposed preview controller design method requires neither special constraints on the state‐space system matrices nor a high‐dimensional augmented error system. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Decentralized robust preview control for uncertain continuous-time interconnected systems

“…Compared with the literatures on tracking control of uncertain continuous-time interconnected systems (Ni et al, 2008;Shigemaru and Wu, 2001), this paper considers that the reference signal is previewable, and the designed controller can make the closed-loop system respond in advance and track the reference signal faster. In addition, compared with the existing results on robust preview control (Li and Liao, 2018;Li et al, 2020), this paper extends robust preview control to the continuous-time systems. The innovations are summarized as follows: (i) The robust preview control for uncertain continuous-time interconnected systems is studied for the first time, and the theory of robust preview control is extended.…”

H∞ model following control of linear parameter‐varying descriptor systems

“…The problem of designing different types of controllers for different classes of descriptor systems has been considered by many researchers. Examples of these controllers are state‐feedback, 2,3 linear quadratic state‐feedback, 4 state‐feedback, 5 state‐feedback, 6 robust state‐feedback, 7 output‐feedback, 8,9 dynamic output‐feedback (DOF), 10 output‐feedback, 11 DOF, 12‐14 DOF, 15 mixed / DOF, 16 dissipative DOF, 17 observer based controller, 18 decentralized static output‐feedback, 19 adaptive controller, 20 Hamiltonian controller, 21 neural network controller, 22 static‐output preview controller, 23 fuzzy controller, 24 sliding‐mode controller, 25 and model predictive controller 26 …”

“…A problem of designing an LPV DOF controller is considered for LPV descriptor systems, where a set of LMI and matrix equality conditions are derived to obtain the control parameters 13 . Moreover, a state‐feedback controller is designed for affine descriptor systems with actuator saturation, 20 and a static output‐feedback controller is designed for discrete‐time uncertain LPV descriptor systems 23 …”

Minimum norm partial eigenstructure assignment problems in high‐order system via feedback control

“…A class of mechanical systems with time invariant characteristics can be described by the following high‐order systems with for . High‐order systems are regarded as more general description forms of linear systems, and are developed from traditional state space systems and descriptor systems 1‐5 . The multiagent systems, power systems, and vibrating structure can be modeled as second‐order systems, while the three‐axis dynamic flight motion simulator systems and the cantilever beam models are often described, respectively, as third‐order and fourth‐order systems using finite element technique 6‐13 .…”

“…with A i ∈ R n×n for i = 0 ∶ k. High-order systems are regarded as more general description forms of linear systems, and are developed from traditional state space systems and descriptor systems. [1][2][3][4][5] The multiagent systems, power systems, and vibrating structure can be modeled as second-order systems, while the three-axis dynamic flight motion simulator systems and the cantilever beam models are often described, respectively, as third-order and fourth-order systems using finite element technique. [6][7][8][9][10][11][12][13] If k = 2, then the systems arise mainly in vibration structure.…”